Finite Group Databasebeta

C2×#19135389 #25100176

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#19135389

Splittings

FittingC22×C4×C8×C43 ⋊ C2
SylowC43 ⋊ C2×#1954

Subgroups

subgroupG/H
centerC23×C4C22×D43
commutatorC22×C43C23×C8
FrattiniC22×C4C23×D43
FittingC22×C4×C8×C43C2
socleC24×C43C22×C4
prime radicalC23×D172C4
cosocleC22×C4×C43C24
hypercenterC22×C4×C8D43
hypocenterC43C2×#1954
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C22×C4×C8

2158 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 173147);